Cross section measurements of neutron elastic and inelastic scattering on ${}^{54}\mathrm{Fe}$

Scattering experiments were performed at the Geel Electron Linear Accelerator (GELINA) to determine the differential cross sections of neutron elastic and inelastic scattering on ${}^{54}\mathrm{Fe}$, using a highly enriched sample. Neutron energies were calculated via the time-of-flight technique. The scattered neutrons were detected using the ELastic and Inelastic Scattering Array (ELISA), a spectrometer consisting of 32 liquid organic scintillators, able to separate neutron and photon induced events via pulse-shape analysis. The detectors are mounted at eight specific angles with respect to the neutron beam direction to allow the concurrent calculation of both the differential and the integral cross section using the Gauss-Legendre quadrature rule. For elastic scattering, angular distributions and integral cross sections were produced in the energy range from 1 to 8 MeV, whereas for inelastic scattering, partial differential and angle integrated cross sections were estimated from the first excited state of ${}^{54}\mathrm{Fe}$ in the energy range from 2.5 to 5.5 MeV. The results are compared with the available experimental and evaluated nuclear data, as well as with theoretical calculations performed with the TALYS 1.9 and EMPIRE 3.2 codes.

Figure 1

The ELISA spectrometer. The neutron beam comes from the right, passing through the fission chamber located behind the lead wall and then it reaches the scattering sample. Here the lead wall acts as the last collimator.

Figure 2

Example of a recorded signal. The time correction based on the CFD algorithm, along with the intervals for the pulse shape discrimination are presented.

Figure 3

The two-dimensional pulse shape discrimination (PSD) spectrum as a function of the light output ($L$) for one of the EJ301 detectors. The black line (DISCRIM.) represents the optimal separation point between neutron (upper part) and photon (lower part) induced events.

Figure 4

Light output distributions for the time-of-flight interval from 1060 to 1065 ns. The graphs correspond to four different detection angles for both the EJ301 $(n,p)$ [(a) to (d)] and EJ315 $(n,d)$ [(e) to (h)] detectors. The experimental values (exp) are presented along with their associated response (model) and their different components from elastic scattering (el) and inelastic scattering (inl) from the first excited stated of ${}^{54}\mathrm{Fe}$ (1.408 MeV).

Figure 5

MCNP version of the ELISA spectrometer. In the geometry, the sample holder, the ${}^{54}\mathrm{Fe}$ disk, the 32 liquid organic scintillators, and their respective mounting are included.

Figure 6

Full pulse height histogram of the ${}^{54}\mathrm{Fe}$ sample-in measurement. The experimental counts (black) are presented along with the corresponding threshold (red) and the plateau region (green) that was used for the linear fit.

Figure 7

Neutron fluence impinged on the ${}^{54}\mathrm{Fe}$ sample with respect to the neutron incident energy. It corresponds to the total duration of the sample-in measurement that amounts to 360 hours.

Figure 8

Angle-integrated cross section of neutron elastic scattering on ${}^{\mathrm{nat}}\mathrm{C}$ as a function of the neutron incident energy compared to other experimental data available in the EXFOR library [10, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57], and the JEFF-3.3 evaluation [4] folded with the experimental energy resolution of the measurement.

Figure 9

Differential cross sections of neutron elastic scattering on ${}^{54}\mathrm{Fe}$ as a function of the neutron incident energy at eight detection angles. The experimental cross sections are compared with the evaluated values provided by JEFF-3.3 [4] and ENDF/B-VIII.0 [58] folded with the experimental energy resolution. The experimental total uncertainties are shown with shadow bars.

Figure 10

Comparison of differential cross sections of neutron elastic scattering on ${}^{54}\mathrm{Fe}$ as a function of the cosine of the scattering angle $\theta$, with data available in literature and the angular distributions provided in the JEFF-3.3 and ENDF/B-VIII.0 evaluations [4, 58]. Six t.o.f. intervals of 5 ns have been selected, that correspond to the following neutron energy ranges: (a) $E=1.494–1.503$ MeV, (b) $E=2.493–2.513$ MeV, (c) $E=3.499–3.532$ MeV, (d) $E=4.973–5.030$ MeV, (e) $E=5.938–6.012$ MeV, (f) $E=6.929–7.023$ MeV.

Figure 11

Angle-integrated cross section of neutron elastic scattering on ${}^{54}\mathrm{Fe}$ as a function of the neutron incident energy compared with data available in the EXFOR library [10], and the JEFF-3.3 and ENDF/B-VIII.0 evaluations [4, 58] folded with the experimental energy resolution of the measurement.

Figure 12

Differential cross sections of neutron inelastic scattering from the first excited state of ${}^{54}\mathrm{Fe}$ as a function of the neutron incident energy at eight detection angles. The experimental cross sections are compared with the evaluated values provided by ENDF/B-VIII.0 [58].

Figure 13

Comparison of differential cross sections of neutron inelastic scattering from the first excited state of ${}^{54}\mathrm{Fe}$ as a function of the cosine of the scattering angle $\theta$, with data available in literature and the angular distributions provided in the ENDF/B-VIII.0 evaluation [58]. The t.o.f. intervals that have been selected correspond to neutrons energy ranges (a) $E=2.750–2.774$ MeV, (b) $E=2.894–2.919$ MeV, (c) $E=2.998–3.023$ MeV, (d) $E=3.973–4.014$ MeV, (e) $E=4.973–5.029$ MeV, (f) $E=5.455–5.521$ MeV.

Figure 14

Angle-integrated cross section of neutron inelastic scattering from the first excited state of ${}^{54}\mathrm{Fe}$ as a function of the neutron incident energy compared with data available in the EXFOR library [10] and the JEFF-3.3 [4] and ENDF/B-VIII.0 evaluations [58]. The experiments in which the $\gamma$-ray emitted from the deexcitation of the first excited state is detected are noted with “-$\gamma$” while the ones in which the neutron is detected are noted with “-$n$”.

Figure 15

Comparison between the theoretical calculations of TALYS [62, 63] using different sets of parameters (see text below), EMPIRE [60] parametrized based on the ENDF/B-VIII.0 [58] evaluation, and the available experimental data in the literature for the ${}^{54}\mathrm{Fe}$ total, elastic, inelastic, $(n,p)$, and $(n,\alpha )$ reaction cross sections. The elastic and inelastic scattering data from this work are also included in the graphs. For the ${}^{54}\mathrm{Fe}(n,n_1^{\prime }$) reaction cross section, a subplot is included focused on the neutron energy region studied in this work.